Wesley and Zane collected some beads. If Wesley gave Zane 66 beads, both would have an equal number of beads. If Zane gave Wesley 42 beads, Wesley would have 5 times as many beads as Zane. Find the number of beads each of them had.
- Wesley?
- Zane?
| Case 1 |
Case 2 |
| Wesley |
Zane |
Wesley |
Zane |
| 3 u + 66 |
3 u - 66 |
5 u - 42 |
1 u + 42 |
| - 66 |
+ 66 |
+ 42 |
- 42 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of beads the same. LCM of 2 and 6 is 6.
The number of beads that Zane had at first is the same in both cases.
3 u - 66 = 1 u + 42
3 u - 1 u = 66 + 42
2 u = 108
1 u = 108 ÷ 2 = 54
Number of beads that Wesley had
= 3 u + 66
= 3 x 54 + 66
= 228
(b)
Number of beads that Zane had
= 3 u - 66
= 3 x 54 - 66
= 96
Answer(s): (a) 228; (b) 96
